The domains of partial attraction of probabilities on groups and on vector spaces

DOI10.1007/BF01046774zbMath0789.60007OpenAlexW2009871575MaRDI QIDQ1209214

Wilfried Hazod, Hans-Peter Scheffler

Publication date: 16 May 1993

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01046774

zbMATH Keywords

stable lawstangent spaceconvolution semigroupsexponential Lie groupssimply connected nilpotent Lie groupdomains of partial attraction

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (8)

\({\mathcal D}\)-domains of attraction of stable measures on stratified Lie groups ⋮ A Gaussian central limit theorem for trimmed products on simply connected step 2-nilpotent Lie groups ⋮ Uniqueness of the embedding continuous convolution semigroup of a Gaussian probability measure on the affine group and an application in mathematical finance ⋮ The accuracy of Gaussian approximations in nilpotent Lie groups ⋮ Uniqueness of embedding of Gaussian probability measures into a continuous convolution semigroup on simply connected nilpotent Lie groups ⋮ Semistable Selfdecomposable Laws on Groups ⋮ Uniqueness of embedding into a Gaussian semigroup and a Poisson semigroup with determinate jump law on a simply connected nilpotent Lie group ⋮ Some new limit theorems for vector space- and group-valued random variables

Cites Work

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• Limit theorems for probability measures on simply connected nilpotent Lie groups
• Continuous automorphism groups on a locally compact group contracting modulo a compact subgroup and applications to stable convolution semigroups
• Automorphisms on a Lie group contracting modulo a compact subgroup and applications to semistable convolution semigroups
• Fourier analysis and limit theorems for convolution semigroups on a locally compact group
• Stetige Faltungshalbgruppen von Wahrscheinlichkeitsmaßen und erzeugende Distributionen
• Operator-Stable Probability Distributions on Vector Groups

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